In any **right angled triangle**, for any angle:

The sine of the angle = __the length of the opposite side__

the length of the hypotenuse

The cosine of the angle = __the length of the adjacent side__

the length of the hypotenuse

The tangent of the angle = __the length of the opposite side__

the length of the adjacent side

The hypotenuse of a right angled triangle is the longest side, which is the one opposite the right angle. The adjacent side is the side which is between the angle in question and the right angle. The opposite side is opposite the angle in question.

sin = o/h cos = a/h tan = o/a

Often remembered by: **soh cah toa**

*Example*:

Find the length of side x in the diagram below:

The angle is 60 degrees. We are given the hypotenuse and need to find the adjacent side. This formula which connects these three is:

cos(angle) = adjacent / hypotenuse

therefore, cos60 = *x* / 13

therefore, *x* = 13 × cos60 = 6.5

therefore the length of side *x* is 6.5cm.

**The graphs of sin, cos and tan**:

The following graphs show the value of sinø, cosø and tanø against ø (ø represents an angle). From the sin graph we can see that sinø = 0 when ø = 0 degrees, 180 degrees and 360 degrees.